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Trapezoid Calculator

Find the area and perimeter of a trapezoid.

How it is calculated

A trapezoid has two parallel sides, the bases a and b, and two other sides c and d (the legs). The tool uses area = (a + b) ÷ 2 × h, where h is the perpendicular height between the bases, and perimeter = a + b + c + d. All five values must be above zero, and they must share one length unit; the area then comes out in that unit squared and the perimeter in that unit. The output labels say "units" because no unit is assumed. The tool does not check that the sides can form a real trapezoid with that height, so make sure the legs are at least as long as the height.

Worked example

Bases a = 10 and b = 6, height 4, legs c = d = 5. Area: (10 + 6) ÷ 2 = 8, and 8 × 4 = 32. Perimeter: 10 + 6 + 5 + 5 = 26. The tool reports area 32.00 units² and perimeter 26.00 units. If the lengths were metres, that is 32 m² of surface and 26 m of edge.

Try this example →

Common mistakes

  • Using a slanted leg as the height. The height is the perpendicular distance between the two bases, which is shorter than either leg unless the leg is vertical.
  • Entering the legs in the base fields. The bases are the parallel sides only; swapping a leg in changes the area.
  • Mixing units, such as bases in metres and height in centimetres. Convert everything to one unit first.
  • Adding the legs to the area formula. The legs only affect the perimeter, not the area.
  • Entering sides that cannot close into a shape. The tool does not verify the geometry and will still give numbers.

About this calculator

A trapezoid has exactly one pair of parallel sides, called the bases (a and b), and its area follows directly from averaging those two bases and multiplying by the height between them: Area = ((a + b) / 2) × h — essentially treating the trapezoid as a rectangle with the "average width" of its two parallel sides. The perimeter simply adds the two bases to the two non-parallel legs.

This shape and formula appear constantly in land surveying and civil engineering, where irregular plots and cross-sections of roads, canals, and retaining walls are frequently trapezoidal; surveyors compute areas of trapezoidal land parcels this way, and hydraulic engineers use the same formula for trapezoidal channel cross-sections in irrigation and drainage design.

Architects sketching roof sections, carpenters cutting trapezoidal panels, and geometry students all rely on this formula because it turns an irregular quadrilateral into a calculation as simple as a rectangle's, once the two parallel sides and the height are known.

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